WEAK SOLUTIONS TO THE PENROSE-FIFE PHASE FIELD MODEL FOR A CLASS OF ADMISSIBLE HEAT-FLUX LAWS

This paper is concerned with a thermodynamically consistent model for diffusive phase transitions proposed by Penrose and Fife. The model ha s recently received a good deal of attention, and the related initial- boundary value problems have been investigated from the mathematical p oint of view. In the case where the order parameter is not conserved, the common working assumption for the heat flow was that such a flux i s proportional to the gradient of the inverse absolute temperature. Th is position seems to be helpful for the analysis, due to the coupling term in the phase-field equation which depends right on the inverse te mperature. Here we prove the existence of weak solutions in a wide set ting of constitutive laws for the heat flux, different from the previo us ones and considerably more significant owing to their behaviour for high temperatures. We also discuss the limiting situation of zero int erfacial energy for the order parameter.